This proposal requests funding for the development of new statistical methodologies for research in survival analysis. The aim of the project is to systematically extend survival analysis in all of its various aspects to handle multivariate data involving censored responses and covariates that may be mixtures of categorical and continuous variables and to do so in a manner that will efficiently balance the model bias and variance in the estimates. The proposal has two projects. The first project considers hazard regression involving univariate censored failure times and multicovaiates that may be continuous, discrete or both. A consistent and unified nonparametric framework will be developed for estimating covariate effects, interactions, hazard and survival functions, even in the absence of proportinality. Sampling properties of the proposed procedures will be studied. Software will be developed to analyze clinical data from cancer and cardiovascular studies. The second project considers the problem of estimating survival and hazard functions for bivariate censored failure times. The project is further divided into two subprojects. The first considers the estimation of the bivariate survival function without covariates. The second considers regression analysis involving covariates that may be mixtures of discrete and continuous variables. The goal is to provide efficient and flexible estimates of covariate effects and bivariate survival functions. Statistical properties of the proposed procedures will be studied. Software will be developed to analyze clinical data from cancer and cardiovascular studies that have bivariate failure times. Finally, the strengths and weaknesses of the proposed procedures will be critically examined by simulations and theoretical investigations.